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dgglse (3)
  • >> dgglse (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dgglse - solve the linear equality-constrained least squares
         (LSE) problem
    
    SYNOPSIS
         SUBROUTINE DGGLSE( M, N, P, A, LDA, B, LDB, C, D,  X,  WORK,
                   LWORK, INFO )
    
         INTEGER INFO, LDA, LDB, LWORK, M, N, P
    
         DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( * ), D(  *  ),
                   WORK( * ), X( * )
    
    
    
         #include <sunperf.h>
    
         void dgglse(int m, int n, int p, double *da, int lda, double
                   *db,  int  ldb, double *dc, double *d, double *dx,
                   int *info) ;
    
    PURPOSE
         DGGLSE solves the linear equality-constrained least  squares
         (LSE) problem:
    
                 minimize || c - A*x ||_2   subject to   B*x = d
    
         where A is an M-by-N matrix, B is a P-by-N matrix,  c  is  a
         given  M-vector,  and  d  is a given P-vector. It is assumed
         that
         P <= N <= M+P, and
    
                  rank(B) = P and  rank( ( A ) ) = N.
                                       ( ( B ) )
    
         These conditions ensure that the LSE problem  has  a  unique
         solution, which is obtained using a GRQ factorization of the
         matrices B and A.
    
    
    ARGUMENTS
         M         (input) INTEGER
                   The number of rows of the matrix A.  M >= 0.
    
         N         (input) INTEGER
                   The number of columns of the matrices A and  B.  N
                   >= 0.
    
         P         (input) INTEGER
                   The number of rows of the matrix B. 0 <= P <= N <=
                   M+P.
    
         A         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDA,N)
                   On entry, the M-by-N matrix A.  On exit, A is des-
                   troyed.
    
         LDA       (input) INTEGER
                   The leading dimension  of  the  array  A.  LDA  >=
                   max(1,M).
    
         B         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDB,N)
                   On entry, the P-by-N matrix B.  On exit, B is des-
                   troyed.
    
         LDB       (input) INTEGER
                   The leading dimension  of  the  array  B.  LDB  >=
                   max(1,P).
    
         C         (input/output) DOUBLE PRECISION  array,  dimension
                   (M)
                   On entry, C contains the right  hand  side  vector
                   for the least squares part of the LSE problem.  On
                   exit, the residual sum of squares for the solution
                   is  given  by the sum of squares of elements N-P+1
                   to M of vector C.
    
         D         (input/output) DOUBLE PRECISION  array,  dimension
                   (P)
                   On entry, D contains the right  hand  side  vector
                   for  the constrained equation.  On exit, D is des-
                   troyed.
    
         X         (output) DOUBLE PRECISION array, dimension (N)
                   On exit, X is the solution of the LSE problem.
    
         WORK      (workspace/output) DOUBLE PRECISION array,  dimen-
                   sion (LWORK)
                   On exit, if INFO = 0, WORK(1) returns the  optimal
                   LWORK.
    
         LWORK     (input) INTEGER
                   The  dimension  of  the  array  WORK.   LWORK   >=
                   max(1,M+N+P).   For  optimum  performance LWORK >=
                   P+min(M,N)+max(M,N)*NB, where NB is an upper bound
                   for  the  optimal  blocksizes  for DGEQRF, SGERQF,
                   DORMQR and SORMRQ.
    
         INFO      (output) INTEGER
                   = 0:  successful exit.
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value.
    
    


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